Erik Kusch, PhD Student
Department of Biology
Section for Ecoinformatics & Biodiversity
Center for Biodiversity Dynamics in a Changing World (BIOCHANGE)
Aarhus University
22/01/2021
[Study Group] Bayesian Statistics with the Rethinking Material 1
22/01/2021
[Study Group] Bayesian Statistics with the Rethinking Material 2
Correlation is not causation!
22/01/2021
[Study Group] Bayesian Statistics with the Rethinking Material 3
Directed edges depict causation!
22/01/2021
[Study Group] Bayesian Statistics with the Rethinking Material 4
The Good:
- Reveal spurious correlations
- Uncover masked associations
The Bad:
- Can cause spurious correlations
- Can hide real associations
Always be mindful of the
variables you use!
The Aim:
In a model with two predictors: “What is the value of one
predictor once we know the value of the other predictor”
Modelling Language:
“How is each predictor related to the response
once we know all other predictors?”
22/01/2021
[Study Group] Bayesian Statistics with the Rethinking Material 5
Standardising variables can make finding priors intuitively
easier.
“Mean divorce rate when all predictors
are at their mean”
Set to be expected at 0 because we
standardised our variables.
“Slopes should not be too strong”
Prior predictive simulations?
22/01/2021
[Study Group] Bayesian Statistics with the Rethinking Material 6
Values on axes are in standard deviations of the
underlying data due to standardisation
Most observations usually fall between +/- 2SD
A prior (x-axis) that predicts the outcome (y-axis) is pretty
infeasible
22/01/2021
[Study Group] Bayesian Statistics with the Rethinking Material 7
Marriage rate is a confound.
Mean divorce rate = 0.00
Slope of marriage rate = -0.07, but very large
standard deviation.
No consistent relationship
Slope of marriage age = -0.61, consistent
Age of marriage drives divorce rate
SD of divorce rate = 0.79
22/01/2021
[Study Group] Bayesian Statistics with the Rethinking Material 8
Prediction does not necessarily need causal understanding.
22/01/2021
[Study Group] Bayesian Statistics with the Rethinking Material 9
Never analyse residuals
themselves!
22/01/2021
[Study Group] Bayesian Statistics with the Rethinking Material 10
Always use samples from the posterior rather
than summary statistics!
Posterior mean
and interval
Prediction is exactly in-
line with observations
Underpredicted divorce rates
22/01/2021
[Study Group] Bayesian Statistics with the Rethinking Material 11
These let you analyse unobserved/impossible cases.
22/01/2021
[Study Group] Bayesian Statistics with the Rethinking Material 12
